The answer to this question will relate the AE analysis in Problem 3 to
the AD-AS diagram we used earlier.

We will start from the answer to Problem 3, part C. At that point,
we had an equilibrium Y of $6000, with I = $460..

Now, if I rises from $460 to $560, we can re-calculate AE, and solve for
equilibrium. But, we already know, using the alternative approach
outlined in
Problem 3, Part D, that a $100 increase in I will lead to a $1000 increase
in equilibrium Y through the multiplier effect.

As is shown in the graph, the equilibrium rises
from Y = $6000 at point E, to Y = $7000 at point F.

The lines shift in AE(Y) to AE(Y)' is caused by
the increase in I, as shown by the increase in autonomous spending fromA to A'.

As AE shifts in the above diagram, AD shifts
to the right in the AD-AS diagram, as shown below:

Point F in the AD-AS diagram above correspond
to point F in the AE diagram. Notice that the new equilibrium value
in the AE diagramis not a short-run equilibrium in the AD-AS
diagram; the AE=Y equilibrium shows a point of aggregate demand, not full
equilibrium in AD-AS space.

A. The quantity of real GDP demanded
rises to $7000.B. In the short run, real GDP does not
rise to $7000, but to the level at point G in the above diagram.
Price increases begin, and that cuts the quantity of real GDP demanded
somewhat over what it would have been, $7000, if the price level had been
constant at P = 100.C. In the long-run, prices will rise unitl
the economy reaches long-run equilibrium at point H, with a price level
higher than P = 100, but the same real GDP as we had originally, $6000.D. Price level rises in the short-run
to the level at Point G.E. Price level rises in the long-run
to the level at Point H. At point H, the real wage is the same as
it was originally, at point E.

NOTE: Though you
were not asked this, you should realize that the horizontal axis on both
of the above diagrams in the same, real GDP.Therefore, to reach short-run equilibrium at
point G in the lower diagram, we must have the AE(Y)' in the upper diagram
shift back somewhat as the price level rises.The higher price level causes the quantity demanded
to drop a bit, from F to G.

Chapter 12:

Problem 1:

Data for the problem: mpc = 0.9 I = $50 G = $40 Tx = $40

We know the reduced form equation for finding equilibrium
real GDP is:

Equilibrium Y = kA and that DY = kDA

If the mpc=0.9, then k = 1/(1-0.9) = 10

A. If G drops from $40 to $30 billion,
the A drops by $10 billion, since

A = a+I+G-mpcTx for this problem; the drop in G is a drop in A.

Therefore, the AE line shifts down by $10 billion in this case.

B. The multiplier is still k = 10.
Therefore, the decline in A of $10 billion would lead to a drop in
equilibrium Y by $100 billion, since DY = kDA.
[$100 = 10[$10 billion]]

C. In this case, if G is maintained
at $40 billion, but Tx is cut to $30 billion, we have:

DA = -mpcDTx = -0.9[-$10
billion] = $9 billion

The drop in taxes of $10 billion leads to an increase in autonomous
spending of $9 Billion, as
consumers increase their consumption spending. The AE line shifts
up
by $9 billion.

This is the balanced budget multiplier effect: With lump-sum
taxes only, if we change G and Tx
by the same amount, then Y changes by that same amount. The multiplier
effect is reduced to
1 = (1-mpc)/(1-mpc).

Problem 2:

A. and B. As we saw above, DY
= kDA, so if A falls by $10 billion, Y will
fall by $100 billion. Therefore, the AE line would shift down by
$10 billion. This means that the AD curve will shift left by
$100 billion, via the multiplier effect.

C. With an upward sloping short-run
aggregate supply curve, real GDP will increase by less than $100 billion
at the new short run equilibrium.

D. In the long run, real GDP will
return to its original level, as resource owners bid-up nominal wages to
restore the real wage.

C. System moves to point d,
a lower price than at b, a higher real GDP than at b.

D. The continued shifting
of the SAS curves leads the system to point e, a lower price level than
at
point a, and a higher real GDP than at point a.
However, this assumes a large supply side effect from
the tax cut.

3. 3. We are given the following
data on consumption spending in a simple economy.

A. Define MPC. Assuming it is constant,
calculate it and use it to fill in the rest of the table. Define
the multiplier. What is its value for this example?

Marginal Propensity to Consumer:
The
change in consumption spending brought about by a change in disposable
income.

mpc = 0.75

B. There are no taxes or transfer
payments or depreciation in this model, for now. But, we have the
following additional data:

Investment Spending = $ 2 million

Government Spending = $ 0.5 million {Only
Federal, no State and
Local}Exports = $ 3 million

Imports = $ 1 million

Given this information, what is the equilibrium
level of GDP?

Autonomous spending
= A = a+I+G+X-IM

a = autonomous consumption spending = $1 million, from the table. Therefore,
using the other data
given in the problem:

A = 1+2+0.5+3-1 = 5.5

k = 1/(1-mpc) = 1/(1-0.75) = 4

Equilibrium Y = kA = 4[5.5] = $22 million.

C. Economists working for the Department
of Commerce predict that next year, imports will rise by $ 2 million, and
exports will rise by only $0.5 million. Assuming that investment
and government spending remain the same, and that the consumption function
remains the same:

a. What will be the new equilibrium
level of GDP next year if these economists have forecasted correctly?

b. What will be the level
of consumption spending at this new equilibrium GDP? What will be
the new level of savings? Is it true that savings equal investment?
Explain.

C = 1+0.75Y
= 1+0.75($16 million) = $13 million.

S = -1+0.25Y
= -1+0.25($16 million) = $3 million.

No,
I = S+(Tx-G)-(X-IM) as before. But, Tx = 0 in this problem.

I = $3 - 0.5 -0.5 = $2, as we see above.

S+(Tx-G)-(X-IM) equals the resources available for use by investors; ie.
total savings in the open
economy. In equilibrium, investment equals this total level of savings.

D. [To answer this question, we will
begin with the data and the results in (B), and ignore what went on in
(C).]

Most members of Congress
agree that the Federal government has run a deficit for long enough, and
that steps must be taken to eliminate it. Two plans have been discussed.
One says to cut government spending from its current level of $0.5 million
to zero. The other says taxes should be raised until the budget is
balanced; assuming only autonomous taxes (sometimes called lump-sum
taxes), this would mean that taxes must be raised from their current level
of zero to $0.5 million.

a. Test each
policy by finding the new equilibrium level of GDP each would bring about.
Why do the equilibrium levels of GDP differ?

If G is cut
from $0.5 to zero, then DA = $0.5 million, and
DY
= kDA = 4[0.5] = $2 million.
So, the new equilibrium would be $20 million.

The equilibria differ
because taxes act through the mpc on consumption. An increase in
taxes of $0.5 million leads to a reduction in autonomous spending of only
$0.375 million, or 75% of the increase in taxes.

b. Discuss the
implications of each policy for the composition of equilibrium GDP, i.e.,
how does the proportion of various goods produced and sold differ under
each scheme, and who is buying them?.

In the first case, when G falls to zero,
we have : C = 1+0.75Y = 1+0.75[$20 million] = $16 million.

In the second case, when Tx is
raised to $0.5 million, C = 1+0.75[Y-Tx} = 1+0.75[$20.5- $0.5] = $16 million.

Therefore, consumers
have the same level of spending in each case. But in the second case,
the government
purchases $0.5 million in
output, paid for by taxes. In the second case, the government has
no role in the economy.

4. We are given the following data for
a simple economy.

[In millions of dollars]Consumption Spending = C = a(r)+0.8*DIa(r)= 100-5r where r - interest
rate in percents
[a(r), autonomous consumption spending, is the component of consumption
spending that does not depend on DI,but
depends on the rate of interest.]

D. If interest rates rise from 10 percent
to 12 percent, find the new level of autonomous consumption, the new level
of investment, and the new value of autonomous spending? What is
the new equilibrium level of GDP?

5. We are given the following information
about an economy: [In millions of dollars]

Consumption Spending = C = a(r)+0.8*DIa(r)= 200-10r where r -
interest rate in percents [a(r), autonomous consumption
spending, is the component of consumption spending that does not depend
on DI, butdepends on the rate of interest.]

B. What is the state of the government
budget? Calculate the surplus or deficit.

Tx-G = 50-500 = -450. There
is a deficit of $450 million.

C. The Congress decides to institute
an income tax in this economy to balance the government's budget.Government spending will not change, but Instead
of having only autonomous taxes, the tax level will bedetermined by the following equation:

Taxes = T0
+ t*Y
Where T0 = 50, as above, and the tax rate, t = 0.25

a.
Write down the equation for the multiplier with an income tax.

With an income tax, the expenditure multiplier becomes k' = 1/[1-mpc(1-t)]

b. For
this particular problem, what is the value of the expenditure multiplier
once the income tax is implemented?

k' = 1/[1-mpc(1-t)] = 1/[1-0.8+0.2]=2.5 In this problem, the
expenditure multiplier is cut in half by the income tax.

c.
Find the equilibrium real GDP after the imposition of the income tax.

Y =k'A(r) = 2.5[735] = $1837.5 million. There is no change in any
autonomous variables, but the slope of the AE
line is reduced.

d. How
did the imposition of the income tax change the government's budget balance;
did the income tax meet
the policy goal set by the Congress? Explain.